The field of the invention is systems and methods for medical imaging, such as magnetic resonance imaging. More particularly, the invention relates to systems and methods for reconstructing a medical image or a series of medical images, such as those obtained with a magnetic resonance imaging system.
Quantitative MRI (“qMRI”) parameter mapping often makes use of analytical models of magnetic resonance signals to offer unique information about tissue microenvironment. This unique information often yields imaging biomarkers that are more sensitive and specific to underlying pathology than regular anatomical MRI. However, most qMRI methods are often too time-consuming because they require multiple measurements along one or more additional parametric dimensions. For example, additional parametric dimensions may include acquiring image data at multiple different echo times for T2 mapping and chemical species separation or at multiple different inversion times for T1 mapping.
The requirement of acquiring measurements along parametric dimensions results in a several-fold increase in scan time, thereby limiting the clinical utility of qMRI techniques. As a result, k-space data is typically undersampled and an advanced reconstruction technique, such as parallel MRI, is used to accelerate qMRI data acquisitions. However, noise amplification, such as g-factor related noise-amplification in parallel MRI reconstruction, limits the practical imaging acceleration to a factor of 2-4 depending on a number of radio frequency (“RF”) receiver coils.
A typical qMRI procedure produces parametric maps by first reconstructing images from acquired k-space data and then performing a pixelwise fit of these images to an analytical model of the underlying magnetic resonance signals. These two stages are decoupled and, as a result, the image reconstruction stage does not benefit from the prior knowledge of the signal behavior in the parametric dimension. In addition, because of this decoupling, errors accumulated during image reconstruction, such as those errors that may be related to undersampling artifacts, resolution loss, and amplified noise, propagate directly into the parametric maps.
One alternative is to directly estimate parametric maps by fitting the signal model to acquired k-space data. If the number of free parameters in the model is less than the number of measurements, sampling of individual datasets can go below the Nyquist limit. However, due to complexity and stability issues of such an estimation, the utility of parametric reconstruction is limited to cases when the signal evolution is described by simple models such as exponential functions.
Another strategy for using prior knowledge is to utilize the analytical signal model to “glue” images in the parametric dimension during reconstruction by relying on the assumption that for each pixel, signal evolution throughout the image series follows a predefined analytical dependence in the parametric dimension. This strategy may be also implemented using different types of linearization to reduce computational burden. If the linearized transform provides a good approximation to the analytical model for a range of target free parameter values, accurate reconstruction is possible in a feasible time. Linearization of the analytical models usually results in more degrees of freedom, which may result in representing a wider range of signals than the range implied by the source analytical models. Yet, such flexibility may come at the expense of constraining power, which limits acceleration capabilities of the techniques.
In currently available qMRI model-based methods, constraining the solution to the signal model happens in a “hard” fashion. That is, the solution is sought among the set of functions that strictly satisfy the chosen model, be it the original nonlinear analytical expression or its linearized version. However, this strategy may lead to detrimental performance due to inaccurate modeling, partial voluming, imaging imperfections, and motion artifacts, which impede accurate estimation of image series and parametric maps and convergence of the algorithms.
The clinical need for high spatial and temporal resolution in time-resolved magnetic resonance applications often necessitates image reconstruction from incomplete datasets because the total scan time is limited due to contrast passage or breath hold requirements. The advent of compressed sensing (“CS”) provided a new sub-Nyquist sampling requirement for images accepting a sparse representation in some basis. However, the limited spatial sparsity of magnetic resonance images affords only moderate acceleration factors before CS-based reconstructions introduce image blurring and blocky artifacts. A better sparsification can be achieved by exploiting spatiotemporal correlations in the time series. In these methods, the underdetermined image reconstruction problem is regularized by making assumptions about the nature of temporal waveforms. The accuracy of reconstruction and achievable acceleration then depends on the validity of these assumptions in practice. In particular, the k-t PCA method, described by H. Pedersen, et al., in “k-t PCA: Temporally Constrained k-t BLAST Reconstruction Using Principal Component Analysis,” Magn. Reson. Med., 2009; 62(3):706-716, postulates that temporal behavior of different image regions can be described by a linear combination of several principal components, which are learned from low-resolution training data. Thus, there remains a need for a method that provides high spatial and temporal resolution images in time-resolved magnetic resonance applications in which incomplete or undersampled data sets are acquired.